Using mass action kinetics via ordinary differential equations to model temporal changes in expression levels of RNAs and proteins in each of many cells in fruit fly embryos, we asked whether experimentally proven interactions among genes and their products could account for the spatio-temporal patterns of gene expression several different genetic modules are known to make during early fruit fly development. It takes many (50 to 100) parameters to quantify the strengths and functional forms of the various interactions among the genes and their products. None has an experimentally measured value so far. So, thinking of this as an inverse problem to be explored numerically, we carried out extensive calculations to sample huge "boxes" in high-dimensional parameter space to get a glimpse of the set of points at which the model network exhibits the same behavior as the real network. We do not yet know much about the ‘shape’ of this point set, but the measure of this set of 'good' points turned out to be unexpectedly huge, corresponding to robustness of the network which would be astonishing were it not essential to make complex genetic modules functionally heritable. We would like to understand, but don't yet understand, how natural selection crafted networks whose spatio-temporal pattern-formation repertoires seems to be encoded mysteriously in the topology of the network's conections, rather than in the strengths/functional forms of those connections. "We" = George von Dassow, Eli Meir, Ed Munro, and me.
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